Problem: Simplify the following expression: $\sqrt{45} + \sqrt{20}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{45} + \sqrt{20}$ $= \sqrt{9 \cdot 5} + \sqrt{4 \cdot 5}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{5} + \sqrt{4} \cdot \sqrt{5}$ $= 3\sqrt{5} + 2\sqrt{5}$ Finally, simplify by combining the terms. $= ( 3 + 2 )\sqrt{5} = 5\sqrt{5}$